ΔfG° are 30.426 kJ/mol for trans-1,2-dichloroethene and 22.112 kJ/mol for cis-1,2-dichloroethene at — Chemical Equilibrium Chemistry Question

💡 Solution & Explanation

Step 1 - Write the isomerization equilibrium and find ΔG° The equilibrium is: \[\text{trans-1,2-dichloroethene} \rightleftharpoons \text{cis-1,2-dichloroethene}\] \[\Delta G°_\text{rxn} = \Delta_f G°(\text{cis}) - \Delta_f G°(\text{trans}) = 22.112 - 30.426 = -8.314\text{ kJ/mol}\] Step 2 - Find K from ΔG° At T = 27°C = 300 K, with R = 8.314 J/(mol·K): \[\Delta G° = -RT \ln K\] \[-8314\text{ J/mol} = -(8.314)(300)\ln K = -2494.2\ln K\] \[\ln K = \frac{8314}{2494.2} = 3.33 = \ln 28\] \[K = 28\] Step 3 - Interpret K to find trans:cis ratio \[K = \frac{[\text{cis}]}{[\text{trans}]} = 28\] This means at equilibrium: [cis] = 28 × [trans]. \[\text{trans : cis} = 1 : 28\] Since cis has lower ΔfG° (22.112 < 30.426 kJ/mol), it is thermodynamically more stable — 28 times more cis than trans at equilibrium. Note: Some printed keys list 28:1, but this is inverted. The physically correct answer is trans:cis = 1:28 (option D). (The answer key says C = 28:1, but that contradicts K = [cis]/[trans] = 28.) Step 4 - Evaluate all options - **Option (A) 10:3**: Incorrect. Does not follow from K = 28. - **Option (B) 3:10**: Incorrect. Does not follow from K = 28. - **Option (C) 28:1**: Incorrect (despite being marked as official key). Would mean [trans] = 28[cis], but K = [cis]/[trans] = 28 gives the opposite. - **Option (D) 1:28**: Correct. K = 28 means [cis]/[trans] = 28, so trans:cis = 1:28.